Devices with fluidic nanofunnels, associated methods, fabrication and analysis systems

ABSTRACT

Methods of forming a chip with fluidic channels include forming (e.g., milling) at least one nanofunnel with a wide end and a narrow end into a planar substrate, the nanofunnel having a length, with width and depth dimensions that both vary over its length and forming (e.g., milling) at least one nanochannel into the planar substrate at an interface adjacent the narrow end of the nanofunnel.

RELATED APPLICATIONS

This application claims the benefit of and priority to U.S. Provisional Application Ser. No. 61/597,364, filed Feb. 10, 2012, the content of which is hereby incorporated by reference as if recited in its entirety herein.

STATEMENT OF FEDERAL SUPPORT

This invention was made with government support under Grant No. R01-HG02647 awarded by the National Human Genome Research Institute. The United States government has certain rights in the invention.

FIELD OF THE INVENTION

This invention relates to fluidics and microelectronic devices.

BACKGROUND OF THE INVENTION

There has been considerable recent interest in the incorporation of nanoscale components in lab-on-a-chip fluidic devices. This interest owes its origin to several advantages (and differences that may be advantageously leveraged) in moving from the micron scale to the nanoscale. These differences can include, for example, one or more of double-layer overlap (DLO) and its effect on electro-osmosis and charge permselectivity, localized enhancement of electric fields, higher surface to volume ratios, confinement effects on large synthetic and biopolymers, and the emerging importance of entropic effects. See, e.g., Yuan et al., Electrophoresis 2007, 28, 595-610; Schoch et al., Rev. Mod. Phys. 2008, 80, 839-883; and Kovarik et al., Anal. Chem. 2009, 81, 7133-7140.

Nanochannels are well suited for a number of applications including single molecule detection and identification, confinement and manipulation of biopolymers, biological assays, restriction mapping of polynucleotides, DNA sizing, physical methods of genomic sequencing, and fundamental studies of the physics of confinement. See, e.g., Riehn et al., Restriction mapping in nanofluidic devices. Proc. Natl. Acad. Sci. USA 2005, 102, 10012; Reccius et al., Conformation, length, and speed measurements of electrodynamically stretched DNA in nanochannels. Biophys. J. 2008, 95, 273; and Cipriany et al., Single molecule epigenetic analysis in a nanofluidic channel. Anal. Chem. 2010, 82, 2480. It is expected that the successful implementation of at least some of the potential applications will require the careful control of molecular dynamics within the nanochannels, including the velocity of molecular transport and the frequency with which analyte molecules are driven through the nanochannels. The transport of a macromolecule from macroscopic and microscopic reservoirs through nanofluidic conduits that are smaller than the molecule's radius of gyration may require the application of a driving force (e.g., hydrodynamic, electrostatic, gravitational) to overcome an energy barrier. This barrier is primarily entropic in nature and can derive from the reduction in the molecule's conformational degrees of freedom in moving from free solution to the confining nanochannel. See, Brochard et al., Dynamics of confined polymer chains. J. Chem. Phys. 1977, 67, 52, Additionally, the probability of a successful transport event can be proportional to the likelihood that the molecule collides with the entrance of the nanofluidic conduit in a conformation favorable to threading. See, Kumar et al., Origin of translocation barriers for polyelectrolyte chains. J. Chem. Phys. 2009, 131, 194903. The practical implication of these fundamental conditions is that molecular transport does not occur until a finite threshold driving force is applied. The magnitude of the requisite force may be considerable, resulting in transport of the analyte through the nanochannel at high velocity. The energy barrier can preclude or inhibit successful transport of the analyte molecule at lower velocity through a nanochannel, such lower analyte velocities may be desirable for many applications.

SUMMARY OF EMBODIMENTS OF THE INVENTION

Embodiments of the invention are directed to devices for fluidic analysis which include at least one nanofunnel, related methods of fabricating, use of the devices and analysis systems.

Some embodiments are directed to methods of forming a chip with fluidic channels. The methods include: (a) forming at least one nanofunnel with a wide end and a narrow end into a planar substrate, the nanofunnel having a length, with width and depth dimensions that both vary over its length; and (b) forming at least one nanochannel and/or microchannel into the planar substrate at an interface adjacent the narrow end of the nanofunnel.

The forming can include milling the nanofunnel that can be carried out using and/or can include defining an electronic patterning file, e.g., a bitmap, stream file, or other computer aided design (CAD) format with desired dimensions. The milling can be carried out using focused ion beam (FIB) milling.

The forming of the at least one nanofunnel and the at least one nanochannel and/or microchannel can both be carried out during a single milling operation using an FIB milling device and a defined electronic patterning file, e.g., bitmap, stream file, or other CAD format to seamlessly connect the nanochannel to the narrow end of the nanofunnel.

The nanofunnel width and depth dimensions can be formed so that they vary in a defined geometric relationship (e.g., parabolic, convex, concave, linear, concatenated funnels) over substantially an entire length of the nanochannel to alter a cross-sectional size of the funnel from the wide end to the narrow end. This change in size may be by at least a factor of two and may vary by at least an order of magnitude.

The defined geometric shape can be a user-defined shape using an electronic patterning file, such as bitmap, stream file, or other CAD format.

The at least one nanochannel can have substantially constant width and depth and the narrow end of the nanofunnel can have width and depth dimensions that substantially match a respective width and depth dimension of an aligned corresponding nanochannel.

The nanofunnel can have a length that is (approximately) between about 1 μm to about 100 μm.

The method can further include sealing a flat cover to the substrate to define a nanofluidic chip adapted to analyze a molecule, such as a biopolymer that can include, for example, DNA molecules and/or proteins.

Other embodiments are directed to devices for analyzing nucleic acids or other molecules. The devices include a nanofluidic chip comprising a plurality of nanofunnels. The nanofunnels have smooth inner surfaces. Each nanofunnel has a wide end and a narrow end and varies (typically gradually) in depth and width along its length. The nanofunnels can each be connected to a respective nanochannel and/or microchannel.

The nanofunnels, where formed by FIB milling, may have at least traces of milling beam projectile material implanted in the nanofunnel inner surfaces.

The nanofunnels can have width and depth dimensions that both vary in a (e.g., user-defined) geometric relationship (e.g., parabolic, convex, concave, linear, concatenated funnels) over substantially an entire length of a respective nanochannel to alter a cross-sectional size of the funnel by at least an order of magnitude from the wide end to the narrow end.

The nanochannels can have a substantially constant width and depth, and the narrow end of the nanofunnels have width and depth dimensions that substantially match a respective width and depth dimension of a corresponding nanochannel.

The forming the nanofunnel step can be carried out by milling. The method can include, before milling the nanofunnel, providing an electronic patterning file that defines dwell times at defined X and Y coordinates to generate the nanofunnel width and depth dimensions over the nanofunnel length. The providing can be carried out to generate a nanofunnel configuration with dimensions with an associated exponent “α” defined by a power law (width, depth ˜x^(α)), where x is an axial coordinate and alpha is a positive number.

The nanofunnel can have a shape with a power law exponent α configured as a function of axial position x, where y˜x^(α(x)). Here “y” is understood to represent either of the dimensions width or depth. In some embodiments, the width and depth may be defined by the same function of x, yielding a nanofunnel with an aspect ratio (depth:width) of 1 along its entire length. In other embodiments, the width and depth may be defined by different functions of x, yielding a nanofunnel with an aspect ratio other than 1 (e.g., 0.1, 0.2, 0.5, 2, 4) along its entire length or an aspect ratio that varies along the nanofunnel's length.

These power laws are exemplary of a variety of geometric relationships and are not exclusive functions defining nanofunnel patterning and forming.

The nanofunnel can have a shape defined by a concatenation of functions (y₁, y₂, y₃, . . . ) where the width and depth of the nanofunnel are defined by y₁ between axial coordinates x₀ and x₁, by y₂ between axial coordinates x₁ and x₂, by y₃ between axial coordinates x₂ and x₃, and so on. Each segment of the nanofunnel can be seamlessly or discontinuously connected to its neighboring segments and the narrow end of the nanofunnel can be seamlessly connected to a corresponding aligned nanochannel or microchannel. The concatenated nanofunnels can consist of 2 to 10 segments in some embodiments or can form long fluidic conduits consisting of 10-100 or even up to hundreds or thousands of segments in other embodiments.

Still other embodiments are directed to methods of analyzing an analyte. The methods can include: (a) providing a chip with at least one nanofunnel that merges into a corresponding nanochannel; (b) applying a first voltage to cause an analyte to flow into a fluid nanofunnel; then (c) applying a second smaller voltage to cause the analyte to flow into a corresponding nanochannel; and (d) electronically or optically analyzing the molecule in the nanofunnel and/or nanochannel.

The method may also include determining molecular identification of the analyte, length of the analyte or localized functionalization mapping based on data from the analyzing step.

The applying step can be carried out so that the flow in the nanochannel is at low velocity.

Yet other embodiments are directed to fluidic analysis systems for analyzing (single) molecules. The systems include: (a) a fluidic chip comprising a plurality of nanofunnels, each funnel merging into at least one respective nanochannel; and (b) a control circuit in communication with the chip configured to (i) apply a first defined transport voltage to cause a molecule to enter at least one nanofunnel then (ii) apply a defined second transport voltage that is less than the first defined transport voltage to cause the molecule to flow into a corresponding nanochannel.

The nanofunnel width and depth dimension can vary in a parabolic relationship over substantially an entire length of the nanochannel to alter a cross-sectional size of the funnel by at least an order of magnitude from the wide end to the narrow end.

At least some of the nanochannels can have substantially constant width and depth, and the narrow end of the nanofunnels can have width and depth dimensions that substantially match a respective width and depth dimension of an aligned nanochannel.

The control circuit of the analysis system can be configured to apply the second transport voltage so that the molecule has a low velocity flow in the nanochannel.

Embodiments of the invention can be configured to allow driving transport at low velocity.

Embodiments of the invention are directed to methods of analyzing a molecule. The methods include: (a) providing a device with at least one nanofunnel; (b) flowably introducing a target molecule into the nanofunnel; (c) trapping the target molecule in the nanofunnel for a time to spatially localize the analyte molecule; and (d) analyzing the analyte molecule in the nanofunnel.

The analyte can include a single DNA molecule. Low fields (E<E_(min)) can momentarily trap DNA molecules but are insufficient to prevent their diffusive escape out of the nanofunnel and away from the nanochannel. Intermediate fields (E>E_(min), E<E_(c)) can stably trap the DNA in the nanofunnel with the position of the DNA molecule (x_(i) and x_(f)) dependent on the magnitude of the electric field. High fields (E>E_(c)) can transport the DNA into and through the nanochannel. Values of the field strengths E_(min) and E_(c) are dependent on the shape and size of the nanofunnel and the size of the DNA molecule.

Embodiments of the invention are directed to a Focused Ion Beam (FIB) milling system. The system includes a FIB milling apparatus in communication with or comprising at least one electronic patterning file configured to generate a nanofunnel in a target substrate.

The FIB milling apparatus is configured to generate any, some or all of the nanofunnel shapes described and/or claimed herein.

Embodiments of the invention can be carried out to evaluate DNA. The method includes obtaining a time-series of images of a single molecule of fluorescently-stained λ-phage DNA fed through a nanofunnel into a nanochannel having a depth dimension that is between about 0.5 nm to about 10 nm, typically between about 1 nm to about 5 nm (e.g., about 3 nm).

It is noted that aspects of the invention described with respect to one embodiment, may be incorporated in a different embodiment although not specifically described relative thereto. That is, all embodiments and/or features of any embodiment can be combined in any way and/or combination. Applicant reserves the right to change any originally filed claim and/or file any new claim accordingly, including the right to be able to amend any originally filed claim to depend from and/or incorporate any feature of any other claim or claims although not originally claimed in that manner. These and other objects and/or aspects of the present invention are explained in detail in the specification set forth below. Further features, advantages and details of the present invention will be appreciated by those of ordinary skill in the art from a reading of the figures and the detailed description of the preferred embodiments that follow, such description being merely illustrative of the present invention.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic illustration of a fluidic analysis device with a funnel-shaped entrance to a nanochannel at one end that intersects or contacts a microchannel used for sample introduction on the other end according to embodiments of the present invention.

FIG. 2 is a schematic illustration of a fluidic analysis device with a plurality of spaced apart nanochannels and respective funnel-shaped entrances according to embodiments of the present invention.

FIG. 3A is a grayscale bitmap image used to pattern a funnel according to embodiments of the present invention.

FIG. 3B is a top view SEM image of the funnel and nanochannel milled into a quartz substrate using the bitmap shown in FIG. 3A according to embodiments of the present invention.

FIG. 3C is a tilted end perspective (about 52 degrees) view of the funnel and nanochannel shown in FIG. 3B illustrating the funnel can decrease in size (width and depth as it approaches the nanochannel.

FIGS. 4A-4C are schematic illustrations of sizing, mapping and sequencing using a prior art nanochannel.

FIGS. 5A and 5B are schematic illustrations comparing DNA transport into nanochannels with (FIG. 5B) and without (FIG. 5A) the use of a funnel according to embodiments of the present invention.

FIG. 6A is a schematic illustration of a fabrication sequence that includes etching, milling and bonding to fabricate a fluidic analysis device according to embodiments of the present invention.

FIG. 6B is a schematic exploded view illustration of a device with stacked substrates according to embodiments of the present invention.

FIGS. 7A-7C are pairs of schematic illustration with corresponding (SEM) images of different exemplary geometric shaped funnel contours according to embodiments of the present invention.

FIG. 8A is a front view of a milling apparatus with an FIB milling mode where each pixel defines where and for how long an ion beam dwells on the substrate according to embodiments of the present invention.

FIG. 8B is a graph of actual depth (nm) versus dwell time for ion beams into substrates that can be used to create nanofunnels according to embodiments of the present invention.

FIG. 9A is a front perspective view of a fluorescence microscope with stained DNA added to reservoirs for fluidic electrokinetic transport through the nanochannels and transport events can be observed using fluorescence microscopy (with the circle inset showing a magnified view of the nanochannel array) according to embodiments of the present invention

FIG. 9B is an image of a series of frames showing transport of fluorescently-stained λ-DNA molecules through a single nanochannel with a funneled entrance according to embodiments of the present invention.

FIGS. 10A-10C are schematic illustrations of nanofunnels and DNA transport at different field strengths according to embodiments of the present invention.

FIG. 11A is a schematic illustration of a nanofunnel with a symmetry axis and dimensional parameters for evaluating suitable electric fields for transport or trapping for various geometries according to embodiments of the present invention.

FIG. 11B is a schematic illustration of different funnel geometries with associated “α” characteristics between 0 and 4 according to embodiments of the present invention.

FIGS. 11C and 11D are graphs of ln V versus ln x for α<0.5 (FIG. 11C) and α>0.5 (FIG. 11D) according to embodiments of the present invention,

FIG. 11E is a schematic illustration of a nanofunnel that has dimensions defined by the proportionality y˜x^(α(x)), where the exponent “α” is itself a function of the axial position x according to embodiments of the present invention.

FIGS. 11F and 11G are schematic illustrations of nanofunnels that have multiple segments (also called multiple portions) where the dimensions in each segment or portion are defined by a different geometric relationship and where neighboring segments or portions are connected seamlessly (FIG. 11F) or discontinuously (FIG. 11G).

FIGS. 12A and 12B are graphs of ln c versus ln x for α<0.5 (FIG. 12A) and α>0.5 (FIG. 12B) with associated exemplary respective nanofunnels holding DNA according to embodiments of the present invention.

FIG. 13A is a graph of x_(i)/b versus qE_(o)D/kT of theory (lines) and simulation results (markers) describing the position of a DNA molecule's leading end (x_(i)) as a function of applied voltage (proportional to E₀, the electric field magnitude in the nanochannel) with values normalized and plotted as dimensionless variables where b is the characteristic DNA Kuhn length, q is the charge on the DNA, D is the geometric average of the nanochannel width and depth, k is Boltzmann's constant, and T is temperature for two different DNA molecule lengths according to embodiments of the present invention.

FIG. 13B is a graph similar to that shown in FIG. 13A but showing the trailing end (x_(f)) according to embodiments of the present invention.

FIG. 14 is a graphical comparison of theory and simulations describing the dependence of the critical electric field required to drive transport through the nanochannel on the power law exponent, a, according to embodiments of the present invention. The dimensionless variable of the plot ordinate is the critical field with the nanofunnel E_(c) ^(f), normalized by the critical field necessary to drive transport through a nanochannel with no funnel, E_(c).

FIG. 15A is a bright field optical image of an exemplary nanofunnel used for a trapping experiment for DNA according to embodiments of the present invention.

FIG. 15B is a fluorescence image of a stained DNA molecule that is stably trapped in the exemplary nanofunnel shown in shown in FIG. 15A

FIG. 15C is a line profile graph of intensity versus x (μm) created from the fluorescence image in FIG. 15B and used to determine the position of the DNA molecule.

FIG. 15D is an image compiled of a series of frames similar to that shown in FIG. 15B, where for each experimental condition (e.g., voltage, DNA length, funnel shape), greater than 20 minutes of data was recorded and position and length information extracted using an analysis program according to embodiments of the present invention.

FIG. 16 is a graph of experimentally determined position x_(o) versus voltage (V) for DNA as shown by the appended image of the DNA in the nanofunnel according to embodiments of the present invention.

FIG. 17 is a graph of experimentally determined position x_(o) versus voltage (V) for DNA for lambda (λ) and T4 DNA with and without PVP (polyvinylpyrrolidone) according to embodiments of the present invention.

FIG. 18 is a graph of experimentally determined length changes (length versus x_(o)) at various voltages for lambda and T4 DNA with and without PVP according to embodiments of the present invention.

FIG. 19 are schematic illustrations of a nanofunnel that merges into the nanochannel with DNA and two alternate drive directions and event frequency according to embodiments of the present invention.

FIG. 20 is a graph of experimentally determined event frequency (min⁻¹) versus voltage (V) with a portion exploded for ease of reference with an appended schematic of the drive direction (funnel side and channel side) according to embodiments of the present invention.

FIG. 21 is an image of a nanochannel illustrating DNA and its concentration at the nanochannel entrance when a voltage less than the energy barrier is applied for a period of time (V=0.5V after about 1.5 hours) according to embodiments of the present invention,

FIG. 22A is an atomic force microscopy image of a funnel interfaced to a nanochannel in which nanofunnel depth is measured at each position whose coordinates correspond to width and length according to embodiments of the present invention.

FIG. 22B is a graph of dimensions (depth, width and area) versus length according to embodiments of the present invention. The measurements of the funnel can be made using the image of FIG. 22A and the cross-sectional area of the funnel can vary linearly along its length.

FIG. 23A is an AFM (atomic force microscopy) image of a funnel with α=0.5 according to embodiments of the present invention.

FIG. 23B is a bit map (BMP) image used to pattern the interface shown in FIG. 23A.

FIG. 23C is an SEM (scanning electron microscope) image of the interface shown in FIG. 23A.

FIG. 24 is a graph of depth, width (μm) versus length x (μm) of exemplary funnel geometry according to embodiments of the present invention.

FIG. 25 is a set of AFM images for funnels having different values of α according to embodiments of the present invention.

FIG. 26A is a graph illustrating a comparison between calculated (theoretical) and experimentally determined positions of the leading and tailing ends of a trapped λ-phage DNA molecule according to embodiments of the present invention.

FIG. 26B is a similar graph illustrating a comparison between calculated (theoretical) and experimentally determined positions of the leading and tailing ends of a trapped T4-phage DNA molecule according to embodiments of the present invention.

FIG. 27 is a schematic illustration of an analysis device/system using a substrate with at least one fluidic nanofunnel and associated channel according to embodiments of the present invention.

FIG. 28 is a schematic illustration of a milling apparatus in communication with and/or including an electronic patterning file for forming desired nanofunnel structures according to embodiments of the present invention.

DESCRIPTION OF EMBODIMENTS OF THE INVENTION

The present invention will now be described more fully hereinafter with reference to the accompanying figures, in which embodiments of the invention are shown. This invention may, however, be embodied in many different forms and should not be construed as limited to the embodiments set forth herein. Like numbers refer to like elements throughout. In the figures, certain layers, components or features may be exaggerated for clarity, and broken lines illustrate optional features or operations unless specified otherwise. In addition, the sequence of operations (or steps) is not limited to the order presented in the figures and/or claims unless specifically indicated otherwise. In the drawings, the thickness of lines, layers, features, components and/or regions may be exaggerated for clarity and broken lines illustrate optional features or operations, unless specified otherwise. In some schematic illustrations, a nanofunnel may be depicted as a two-dimensional projection to clearly depict the nanofunnel shape. It should be understood that width and depth dimensions can both vary over the nanofunnel's length.

The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. As used herein, the singular forms, “a”, “an” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms “comprises,” “comprising,” “includes,” and/or “including” when used in this specification, specify the presence of stated features, regions, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, regions, steps, operations, elements, components, and/or groups thereof. As used herein, the term “and/or” includes any and all combinations of one or more of the associated listed items. As used herein, phrases such as “between X and Y” and “between about X and Y” should be interpreted to include X and Y. As used herein, phrases such as “between about X and Y” mean “between about X and about Y.” As used herein, phrases such as “from about X to Y” mean “from about X to about Y.”

It will be understood that when a feature, such as a layer, region or substrate, is referred to as being “on” another feature or element, it can be directly on the other feature or element or intervening features and/or elements may also be present. In contrast, when an element is referred to as being “directly on” another feature or element, there are no intervening elements present. It will also be understood that, when a feature or element is referred to as being “connected”, “attached” or “coupled” to another feature or element, it can be directly connected, attached or coupled to the other element or intervening elements may be present. In contrast, when a feature or element is referred to as being “directly connected”, “directly attached” or “directly coupled” to another element, there are no intervening elements present. Although described or shown with respect to one embodiment, the features so described or shown can apply to other embodiments.

Unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the present application and relevant art and should not be interpreted in an idealized or overly formal sense unless expressly so defined herein. Well-known functions or constructions may not be described in detail for brevity and/or clarity.

Spatially relative terms, such as “under”, “below”, “lower”, “over”, “upper” and the like, may be used herein for ease of description to describe one element or feature's relationship to another element(s) or feature(s) as illustrated in the figures. It will be understood that the spatially relative terms are intended to encompass different orientations of the device in use or operation in addition to the orientation depicted in the figures. For example, if the device in the figures is inverted, elements described as “under” or “beneath” other elements or features would then be oriented “over” the other elements or features. Thus, the exemplary term “under” can encompass both an orientation of over and under. The device may be otherwise oriented (rotated 90 degrees or at other orientations) and the spatially relative descriptors used herein interpreted accordingly. Similarly, the terms “upwardly”, “downwardly”, “vertical”, “horizontal” and the like are used herein for the purpose of explanation only unless specifically indicated otherwise.

It will be understood that, although the terms first, second, etc. may be used herein to describe various elements, components, regions, layers and/or sections, these elements, components, regions, layers and/or sections should not be limited by these terms. These terms are only used to distinguish one element, component, region, layer or section from another region, layer or section. Thus, a first element, component, region, layer or section discussed below could be termed a second element, component, region, layer or section without departing from the teachings of the present invention.

The term “about” refers to a dimension or other parameter that is close to but not exactly the associated dimension or other parameter value or number, typically within about +/−20% or less, such as about +/−10% or less, than that dimension or other parameter value or number.

The term “gradually” with respect to a change in shape of a respective nanofunnel according to some particular embodiments refers to a shape that tapers inward to a smaller size.

Generally stated, embodiments of the application provide techniques using milling to fabricate nanofunnels, and optionally nanochannels, with primary (sometimes described as “critical”) dimensions. The term “milling” refers to any process that forms channels using a charged particle or particles. Thus, while some examples are described herein with respect to a Focused Ion Beam (FIB) milling process, other milling processes may be used including those that employ Ar⁺ ion beams, proton beams, He ion beams, Ga⁺, In⁺, C₆₀ ⁺, and electron beam milling. The term “implanted projectiles” refers to the particles implanted in the substrate nanofunnels or nanochannels in response to the milling process (based on the type of beam used to form the nanochannel). In some embodiments, devices used to analyze (fluidic) samples can comprise implanted projectiles that may be present in a trace amount (detectable with SEM or other evaluation methods), present in larger amounts or removed (e.g., via known subsequent processing techniques). The milling can be carried out to alternate charged particle milling with charged particle induced deposition processes that allows redeposition of masking material during the milling process. The redeposition of masking materials can allow for a renewal of the masking material during the etching process enabling greater aspect ratio nanochannels to be produced. The deposition of solid phase materials using focused particle beams and volatile precursor molecules is a well-established technique. (see S. J. Randolph, et al., Crit. Rev. Solid State Mat. Sci., 2006, 31, 55-89, the contents of which are hereby incorporated by reference as if recited in full herein.) A broad range of metals, insulators, and semiconductor materials can be deposited using these technique including Cr, Pt, Si and/or SiO₂. The redeposition process may be particularly important when milling the narrowest high-aspect ratio funnels and/or channels. These funnels and/or channels can be milled by rastering the charged particle beam across an area and/or along a line. Precursor gas of the deposited material can be injected at appropriate intervals during the beam rastering to achieve the desired nanochannel dimensions.

The term “electronic patterning file” refers to electronic (programmatic) instructions typically held in one file, but may be distributed in more than one file and on local or remote computers, to define a target nanofunnel formation pattern or image that can be used for a fabrication device such as for a milling mode of a milling instrument. The electronic patterning file can comprise one or more CAD (computer-aided design) files with milling instrument instructions/controls as to ion beam dwell time and intensity and the like. The term “bitmap” refers to computer-implemented instructions of a desired milling pattern or image for a milling mode for a milling instrument, such as an FIB milling instrument, where each pixel defines where and for how long an ion beam dwells on a target substrate. The term “stream file” refers to an ASCII text or binary file that defines the ion beam dwell time for each of a set of x, y coordinates (pixels), as listed in the file. As will be recognized by one of skill in the art, the functionality of the bitmap and stream file is the same but a bitmap is a matrix while the stream file is a list which can have subtle differences as to how the instrument patterns from the respective files.

It is noted that while the following examples describe the use of milling, and particularly, FIB milling, to form the nanofunnel, the nanofunnel and/or nanochannel (or microchannel) can be formed using any suitable apparatus or fabrication technology including for example milling, etching, molding, and embossing or combinations of the different fabrication technologies. For example, a first complementary feature can be formed, e.g., etched or milled on/in a target substrate, then the funnel construct can be formed by molding or embossing over or about the complementary feature.

The term “power law” refers to a mathematical model of nanofunnel shape and dimensions characterized by an exponential factor “alpha” where the nanochannel width (w) and depth (d) vary with position along the nanofunnel's longitudinal axis (x) by the power law w, d˜x^(α). This power law may sometimes be described as y˜x^(α), where it is understood that “y” represents the width and/or depth of the nanofunnel. The width and depth may be defined by the same function of x, yielding a nanofunnel with an aspect ratio (depth:width) of 1 along its entire length. The width and depth may be defined by different functions of x, yielding a nanofunnel with an aspect ratio other than 1 (e.g., 0.1, 0.2, 0.5, 2, 4) along its entire length or an aspect ratio that varies along the nanofunnel's length. The power laws described herein are exemplary of a variety of geometric relationships and are not exclusive functions defining nanofunnel patterning and forming.

The term “nanofunnel” refers to a fluidic channel that has a three-dimensional funnel shape with two opposing ends, with one end having a wide end with a wider opening and the other opposing narrow end having a narrower opening, with the narrow end having at least one primary dimension (width and/or depth) with a nanometer size. The funnel shape may be substantially conical or frustoconical, concave or convex, but is typically formed in one or two overlying, cooperating flat substrates so that the funnel depth and width taper inward to narrow in width and also to become more shallow in depth along one direction, which may be in a flow or reverse flow direction. In some embodiments, the funnel shape can be configured to gradually decrease in cross-sectional size by at least an order of magnitude along the transit path, with the smallest dimensions being substantially equal to those of a nanochannel with which they can be seamlessly integrated (and merge into). The term “primary dimension” in the singular refers to a width and/or depth dimension with the term used in the plural to include both the width and depth dimensions. The primary dimensions of the nanofunnel at the narrow end are both typically below about 50 nm, including about 25 nm or less (on average or at a maxima), such as between about 1 nm to about 25 nm and any value therebetween, including about 5 nm, about 10 nm, about 15 nm, about 20 nm and about 25 nm. The length of the nanofunnel(s) can vary typically according to end application. These applications can include, for example, but are not limited to, a device that includes a nanofunnel that merges into a nanochannel, a device that includes a nanofunnel that connects a nanochannel with a microchannel, a device that has a nanofunnel that joins two closely spaced apart microchannels, or a device that has a nanofunnel in fluid communication with a microreservoir.

The term “nanochannels” refers to an elongate channel with sidewalls and a floor, sometimes also referred to as a “trench”. The term “microchannels” refers to channels that are small but larger than nanochannels. The primary dimensions of the nanochannel(s) are both typically below about 10 nm, including about 5 nm or less (on average or at a maxima). In some embodiments, the depth and/or width can be about 3 nm or less, e.g., about 1 nm. In some embodiments, the depth is between about 1 nm to about 10 nm (on average or at a maxima) and the width is the same or larger (e.g., between about 2-10 times larger) than the depth dimension, again either measured on average or as a maxima. In other embodiments, the nanochannel can have primary dimensions up to about 100 nm. The length of the nanochannels can vary typically according to end application. However, in some embodiments the nanochannels can have a relatively short length such as about 100 nm, but are typically between about 10 microns to 100 microns. In other embodiments, the nanochannels can be longer, such as between about 0.5-12 inches (particularly when using stitching or continuous precisely controlled movements of a sample stage while milling), although are more typically between about 0.5-2 inches. The nanochannels may be linear or extend along an axis in a spiral, serpentine or other curvilinear pattern.

The nanofunnel(s) and, where used, nanochannels, can be formed into at least one solid planar substrate to have an open top surface and a closed bottom surface with the sidewalls extending therebetween. A cover may be used to seal or otherwise close the upper surface of the nanofunnel and nanochannel. The nanochannels can be configured with an aspect ratio (AR) of about 1 (e.g., the average width and average depth are substantially the same or do not vary more than about 20%) but may also have other aspect ratios, typically with the width dimension being 2-10 times greater than the depth dimension, e.g., such as an AR of about 1:3 (H (depth dimension):W). In some embodiments, the nanochannels can include aspects greater than 1, but less than 10.

The term “low velocity” refers to a velocity associated with movement of a sample, e.g., single molecule, through a nanochannel at velocities below about 0.01 cm/s. The term “low voltage driving force” refers to the voltage applied using electrodes in communication with a flow transit channel to drive transport of a sample, e.g., a molecule, into and/or through a respective nanofunnel and/or nanochannel. The low voltage driving force can be described in absolute terms or in terms of length of a fluid channel, e.g., nanochannel or nanofunnel. The low voltage driving force for a nanofunnel, where used, can be under about 5V, typically under about 1V, and for a nanochannel can be lower such as about 500 mV or less. Typically, one driving voltage is applied to drive a sample into a respective nanofunnel, typically between about 1-5V, then a smaller second voltage can be applied to move the sample into a nanochannel, the second voltage typically being below about 500 mV, such as, for example, between about 300 mV to about 200 mV.

Turning now to the figures, FIG. 1 is a schematic illustration of one embodiment of a device 10. As shown, the device 10 has a planar substrate 10 p with a microchannel 15, a nanofunnel 20 and a nanochannel 30. In the embodiment shown, the nanofunnel 20 has a narrow end 20 n that defines a funnel-shaped entrance into a respective aligned nanochannel 30. The wide end of the funnel 20 w can reside proximate a microchannel used for fluidic sample introduction. The nanochannel 30 can have a length that is much greater than the length of the funnel 20, typically at least three times greater and more typically greater than about 5 times, 6 times, 7 times, 8 times, 9 times, 10 times or even greater length. In some embodiments, the nanofunnels 20 can have a relatively short length such as about 100 μm or less, typically between about 100 nm to about 50 μm, including about 75 μM, about 50 μm, about 25 μm, about 15 μm, about 10 μm, about 1 μm, about 500 nm, and about 100 nm or any number therebetween. In some embodiments, the length can be less than 100 nm, such as about 75 nm, about 50 nm, about 25 nm or less and any number therebetween.

Referring to FIG. 2, the device 10 can include at least one nanofunnel 20, but typically includes a plurality of spaced apart nanofunnels 20. Although shown as two spaced apart nanofunnels 20 ₁, 20 ₂, the device 10 can include more than two nanofunnels. As shown, each nanofunnel 20 ₁, 20 ₂ can merge into a respective nanochannel 30 ₁, 30 ₂ or connect other fluid structures.

The nanofunnel 20 can be configured to have dimensions in both width and depth (also described as “height”) that gradually decrease by over at least an order of magnitude along the transit path. In some embodiments, the narrow end 20 n with the smallest dimensions can be substantially equal to and aligned with those of a corresponding nanochannel 30 with which they can be (seamlessly) integrated.

FIG. 3A is a grayscale bitmap image used to pattern a funnel with gradually varying width and depth over its length 20 l. FIG. 3B is a top view SEM (Scanning Electron Microscope) image of a funnel 20 and a first end of a corresponding nanochannel 30 milled into a quartz substrate using the bitmap 20 bm shown in FIG. 3A. FIG. 3C is a top, end perspective view (tilted at 52 degrees) of the funnel and nanochannel shown in FIG. 3B illustrating the varying depth (in the length direction). In this embodiment, the funnel 20 decreases in size from about 1.5 μm×about 1.5 μm (width×depth) to about 25 nm×about 25 nm (width×depth). However, other funnel geometry and dimensions may be used.

In some embodiments, the funnels 20 can be configured to lower the threshold force needed to drive transport. This can be achieved by the gradual increase in the degree of confinement experienced by an analyte molecule as it moves along the length of the funnel 20. This effect, in combination with a force gradient that may partially be attributed to the funnel geometry, can effectively “precondition” the analyte molecule, resulting in a conformation conducive to threading into the nanochannel 30.

FIGS. 4A-C and 5A illustrate a nanochannel 30 with a fluid reservoir 60 with an analyte 40 (DNA), and without a funnel 20, which can be used for mapping, sizing and sequencing DNA. See also, Levy et al., Chem Soc Rev 39 2010, 1133; Lagerqvist et al., Nano Lett, 6 2006, 779, and U.S. Provisional Application Ser. No. 61/384,738, filed Sep. 21, 2010 (and corresponding pending PCT/US2011/052127) the contents of which are incorporated by reference as if recited in full herein. FIG. 5B illustrates the device 10 with the nanofunnel 20 that can provide an entry path for the analyte 40.

FIG. 6A illustrates a series of operations (A-C) that can be used to form devices 10 with at least one funnel 20 using milling, typically FIB milling. It is noted that the sequence of A and B may be reversed. The planar substrate 10 p of the device 10 funnel(s) 20 can be processed to include one or more microfluidic channels 15 that can be prepared using standard photolithographic and etching techniques or other techniques (operation “A”). Next, FIB milling can be used to form an interface with a funnel 20 and nanochannel 30 in the substrate 10 p. The funnel and nanochannel 20, 30 can be seamless and connect to the channels 15 to be in fluid communication with the channels 15 and reservoirs 60 (operation “B”).

The device 10 can be a compact “chip”-like device with multiple nanofunnels 20 and nanochannels 30 and one or more associated reservoirs 60. The reservoir(s) 60 may have a short cylindrical configuration or other configuration and may be externally accessible (FIG. 6A). The term “chip” refers to a substantially flat compact body with integrated fluidic structures. The chip can be any geometric shape but is typically polygonal, such as substantially square or substantially rectangular. The chip can be in different sizes but typically has an area that is less than about 10 in² (e.g., about 25 mm×25 mm).

FIG. 6A also illustrates that electrodes 70 can be attached to the device 10, typically with positive and negative polarity at spaced apart respective reservoirs 60 to drive the transport of the fluid analyte (e.g., molecule) through the fluidic structures as is well known.

In some embodiments, the device 10 can be configured for analyzing molecules, such as nucleic acids. The device 10 can be a nanofluidic chip comprising a plurality of nanofunnels 20, each connected to a respective nanochannel 20. The nanofunnels 20 and nanochannels 30 can have a smooth inner surface (from the milling process into the substrate). The nanofunnels 20 and the nanochannels 30 can include at least traces of implanted milling projectiles from a milling beam used to form the nanofunnels 20 and the nanochannels 30. The interface between a respective nanofunnel 20 and channel 30 can be seamless in that the narrow end of the funnel 20 can have the same dimensions as the nanochannel 30. The nanochannel 30 can have a constant width and depth over at least a major portion of its length and typically over its entire length. The nanochannel 30 can be formed during a single milling operation as continuation of the milling process used to form the nanofunnel 20 or vice versa (e.g., the nanochannel can be formed first and the nanofunnel can be a continuation of that process). The term “seamless” means that there is not a seam that adjoins the two features.

The device 10 can have a planar substrate 10 p of a variety of substrate materials, allowing device fabrication in glass, quartz, silicon, ceramics, metals, plastics, etc. In the case of electrically insulating substrate materials, FIB milling can be performed through a relatively thick (>100 nm) high quality metal film deposited on the top surface of the substrate. This metal film prevents charging during the milling process and allows milling of features with suitable tolerances and can allow critical dimensions that extend below 5 nm. See, e.g., U.S. Provisional Application Ser. No. 61/384,738, filed Sep. 21, 2010 and corresponding pending PCT/US2011/052127, and Menard, L. D.; Ramsey, J. M., The fabrication of sub-5-nm nanochannels in insulating substrates using focused ion beam milling. Nano Lett. 2011, 11, 512, the contents of which are incorporated by reference as if recited in full herein.

FIGS. 7A-7C illustrates different exemplary geometric shaped funnel contours 20 c. FIG. 7A illustrates that the nanofunnel 20 has a convex contour 20 cv. FIG. 7B illustrates the funnel 20 has a straight line taper with walls tapering in at a (substantially) constant slope. FIG. 7C show a nanofunnel 20 with a concave contour 20 con. FIG. 23 illustrates that the nanofunnel 20 can have a substantially parabolic relationship/shape.

At “B”, nanochannels 30 of a substantially constant depth can be fabricated by rastering the ion beam over a rectangular area or along a line, with each point in the rectangle or line exposed to the same ion dose. Deeper (funnel) channels can be milled by defining higher ion doses while shallower channels can be milled using lower ion doses. FIG. 8A shows an example of an FIB milling device with a BMP milling mode where each pixel can define where and how long an ion beam dwells on the substrate 10 p. FIG. 8B illustrates an example of depth (nm) that can be set by dwell time (typically between about 1 μs to about 10 ms per pixel) with an appended gray scale graduated graph of dwell time resulting in increased depth. Because FIB milling is a direct write process, features that are relatively complex can be patterned, as described below. After FIB milling and removal of the metal film from the substrate (if used), the fluidic network comprising a funnel 20 can be sealed by bonding a cover plate 50 (operation “C”) on top of the substrate using one of several possible methods such as fusion, anodic, or adhesive bonding.

In the embodiment shown in FIG. 6A, the use of two planar cooperating substrates results with the funnel formed only in the bottom substrate 10 p results in a flat top face to the funnels 20, regardless of the geometry milled into the substrate 10 p. FIG. 6B shows an embodiment where the funnels 20 can be configured so that both width and depth vary gradually and symmetrically around the long axis of the funnel 20. This configuration can be fabricated by milling identical funnel features and optionally a portion or all of the nanochannel 30, in both the top and bottom substrates 50, 10 p, followed by bonding of the two substrates with precise alignment.

It is noted that prototypes of the device 10 were fabricated in quartz substrates because of quartz's suitability for microfluidic and nanofluidic devices. However, FIB milling of nanofluidic structures can be extended to various hard and soft materials as described in the U.S. Provisional Application Ser. No. 61/384,738, filed Sep. 21, 2010 and corresponding pending PCT/US2011/052127, which has been incorporated by reference. Examples of hard materials include, but are not limited to, substrates comprising one or combinations of: glass, quartz, silicon, and silicon nitride. The soft materials can have a low Young's Modulus value. For example, elastomers and harder plastics and/or polymers can have a range between about 0.1-3000 MPa. Examples of soft materials include, but are not limited to, polydimethylsiloxane (PDMS), polymethylmethacrylate (PMMA), and polyurethane.

As shown in FIG. 8A, a milling apparatus 200 can be configured to generate a desired shape of a nanofunnel 20 in a substrate 10. An electronic patterning file 200 f (which can be provided in a number of manners including, for example, by one or more of an ASIC (Application Specific Integrated Circuit), an application (“APP”), a module and/or subdirectory file of a controller or digital signal processor) that can be held in the milling apparatus 200 or the milling apparatus 200. Alternatively, the apparatus 200 can be controlled or have access to at least one external (local or remote) device such as a processor with the electronic patterning file 200 f that can generate a desired funnel shape in the substrate 10. The electronic patterning file 200 f can also be distributed over various components and locations. The electronic patterning file 200 f can define the dwell time per pixel of the milling beam 200 b (FIG. 8B) over X, Y coordinates, or other defined coordinate systems to generate a defined nanofunnel shape. The electronic patterning file 200 f can be configured as selectable different patterning instructions correlated to one or more of the following: (i) different substrate materials; (ii) different nanofunnel shapes and/or dimensions; or (iii) different target analytes.

The milling apparatus 200 can include a control circuit 200 c that can communicate with at least one remote or local processor via a local area network (LAN), a wide area network (WAN) or via a global computer network, e.g., the Internet to obtain or use the electronic patterning file 200 f. The milling apparatus 200 can be an FIB milling apparatus.

As shown in FIG. 28, a fabrication system 201 can comprise the apparatus 200 can include a control module or circuit 200 c that can be onboard the apparatus or at least partially remote from the apparatus. If the latter, the control module or circuit 200 c can reside totally or partially on a server 225 (FIG. 28). The server 225 can be provided using cloud computing which includes the provision of computational resources on demand via a computer network.

Referring to FIGS. 8A and 8B, according to some embodiments, FIB milling can be performed using a Helios NanoLab DualB earn Instrument (FEI Company) with a Ga⁺ ion source operated at about 30 kV. This instrument is capable of using bitmap image files (20 bm, FIG. 5A-7C) to define a milling pattern. The x and y coordinates of the image define where the ion beam dwells during the scan, thus achieving milling, and the gray-scale value of the pixel (0 to 255) defines the length of time that the ion beam dwells on the region of the sample corresponding to the pixel. The operator or a default configuration of the apparatus 200 and/or the electronic patterning file 200 f can define the maximum dwell time, t_(max). White pixels (gray-scale value equal to 255) can be exposed for a milling time of t_(max) while black pixels (gray-scale value equal to 0) are not exposed to the ion beam and thus are not milled. Pixels with intermediate values on the gray scale can be milled for a fraction of t_(max), where the length of exposure is linearly dependent on the gray-scale value (e.g., the dwell time at a pixel with a gray-scale value of 125 is 125/255*t_(max)=0.49*t_(max)). Color scale pixels may be used in the future.

FIGS. 3B-3C show representative scanning electron microscopy (SEM) images of a funnel with varying depth and width interfaced to a nanofluidic channel. As discussed above, FIG. 3A is an image of the original bitmap file 20 bm used to mill the funnel and channel features shown in FIGS. 3B and 3C.

Measuring the Electrophoretic Mobility of DNA in 25-nm Nanochannels

A series of experiments were carried out to determine the electrophoretic mobility of double-stranded DNA through 50-μm long channels having dimensions of 25 nm×25 nm (width×depth). These consisted of electrokinetically driving single λ-phage DNA molecules from one microfluidic reservoir to another through an array of nanochannels (FIG. 9A). FIG. 9A is a schematic illustration that shows an experimental setup where stained DNA solutions are added to the device reservoirs 60, DNA is electrokinetically driven via electrodes and electric field(s) through the nanochannels 30, and transport events are observed using fluorescence microscopy using a microscope 230. The inset shows a magnified view of the nanochannel array. The DNA was stained with an intercalating fluorescent dye (YOYO-1, Invitrogen) at a base pair to dye molecule ratio of 5:1. Fluorescence was excited by light from a mercury arc lamp passing through an excitation filter and a 100× oil-immersion plan apochromatic objective lens. Fluorescence from single molecules was collected through the 100× lens and imaged using an electron-multiplying CCD camera (Cascade II, Photometrics). This high sensitivity camera can collect images at frame rates up to 400 frames per second. Image analysis of individual, time-stamped frames provided information on single molecule dynamics such as molecular extension and the velocity of transport.

However, it was found that initiating translocation of the DNA molecules through nanochannels of this size required electric field strengths in the nanochannels of at least 1000 V/cm. In practice, field strengths exceeding 3000 V/cm were required to drive events with sufficient frequency to analyze a statistically significant sample of molecules. This corresponded to a velocity of ˜0.9 cm/s, meaning that during translocation of the molecule through a 50-μm long nanochannel, fewer than three frames were captured. This limited data, in combination with the finite length of the λ-DNA molecules (˜20 μm when stained) and the potential for image artifacts caused by the molecules' high velocity precluded the determination of electrophoretic mobility.

In order to lower the threshold field strength to initiate the threading of single DNA molecules into the about 25 nm×25 nm channels, a device with nanochannels having identical critical dimensions but with funneled entrances was fabricated. The funnel cross-section gradually decreased in size from about 350 nm×350 nm to 25 nm×25 nm over a length of about 5 μm. The change in width and depth can be defined by a parabolic function (FIG. 7C). An SEM image of one of these nanochannel entrances is shown in the inset in FIG. 9B (top right of the figure). The threshold field strength (in the nanochannels) required to drive DNA translocation through the nanochannels in this device was about 350 V/cm, or three-fold lower than the device without funneled entrances. Consequently, it was possible to record a greater number of frames for a single translocation event and analyze these frames to determine the dynamics of transport. A representative series of frames showing transport through one of the 25-nm nanochannels with a funneled entrance is shown in FIG. 9B. Here, it is clear that the DNA molecule enters into the funnel where it slowly elongates into a configuration that then threads into the 25-nm nanochannel. In the absence of the confining funnel and at a comparable field strength, this threading process would likely progress too slowly to ensure translocation before the DNA molecule diffused away from the nanochannel entrance.

FIG. 9B illustrates a series of frames showing the transport of fluorescently-stained λ-DNA molecules through a single 25-nm nanochannel with a funneled entrance. The inset SEM image shows the entrance of this nanochannel. The vertically oriented dashed lines indicate, from left to right, the entrance to the funnel, the funnel to nanochannel interface, and the other end of the nanochannel 30.

Threshold Lowering and Stable DNA Capture

The FIB milling process affords considerable flexibility in the shape and dimension of funnels 20 that can be used to interface the microfluidic and nanofluidic components on a device 10. It is contemplated that funnel geometries can be selected to minimize the applied forces, making low velocity transport possible. This may be accomplished by calculating the force applied to the DNA molecule in the nanochannel under conditions where the entropic force of the molecule's gradual confinement in the funnel is balanced by the driving force in the funnel supplied by the applied voltage, pressure, or gravitational field. Additionally, the presence of the two opposing forces may result in a range of applied voltage, pressure, or centripetal force over which a DNA molecule can be trapped in the funnel indefinitely if appropriate funnel geometries are used.

Optimal nanofunnel geometries can be determined by the theoretical modeling of DNA molecules subjected to the appropriate entropic and driving forces. In the following examples, DNA molecules are driven into and through the nanofunnels and nanochannels using an applied voltage. Similar modeling could be readily performed in which the driving force was an applied pressure or centripetal force, for example. FIGS. 10A-10C illustrate the information obtainable from these theoretical calculations. For a given funnel geometry, there is a minimum electric field strength (E_(min)) that must be applied to force the DNA molecule into the nanofunnel 20. Above this field strength and for some nanofunnel geometries, the DNA molecule can be stably trapped in the nanofunnel 20. As the voltage is increased, the average position of the molecule moves towards the nanochannel 30. When the electric field strength exceeds a critical value (E_(c)) the DNA molecule is forced out of the trap and is transported through the nanochannel 30. Theoretical modeling can determine the characteristic field strengths (E_(min), E_(c)) that define the stable trapping regime, the average position of a trapped DNA molecule (x_(i), x_(f)), its extended length (x_(f)−x_(i)), and the critical voltage that must be applied to drive transport through the nanochannel (E_(c)).

Low fields (E<E_(min)) can momentarily trap DNA molecules but are insufficient to prevent their diffusive escape out of the nanofunnel 20 and away from the nanochannel 30. Intermediate fields (E>E_(min), E<E_(c)) can stably trap the DNA in the nanofunnel 20 with the position of the DNA molecule (x_(i) and x_(f)) dependent on the magnitude of the electric field. High fields (E>E_(c)) can transport the DNA into and through the nanochannel 30. The values of the field strengths E_(min) and E_(c) are dependent on the shape and size of the nanofunnel and the size of the DNA molecule. For this reason, a theoretical understanding of DNA behavior in a nanofunnel, according to embodiments of the invention, can be important for establishing these values a priori.

Different nanofunnel shapes can be configured to be optimal for different functions. For example, one nanofunnel can dramatically reduce the voltage required to drive transport into its associated nanochannel, resulting in low velocity DNA transport. The same nanofunnel may have a very limited range of voltages over which the DNA molecule is stably trapped. In contrast, a second nanofunnel can be optimized to have a large range of voltages over which trapping in the nanofunnel is stable. This second nanofunnel may require a higher critical voltage, however, to initiate DNA transport through the nanochannel. FIGS. 11A-D illustrate some elements of nanofunnel shape that have been investigated. The nanochannel width (w) and depth (d) vary with position along the nanofunnel's longitudinal axis (x) by the power law w,d˜x^(α).

In some particular embodiments, Equation 1 can be used to define how the nanofunnel width and depth vary as a function of position along the nanofunnel raised to exponent “α”, again based on the desired nanofunnel operational characteristics. In Equation 1, the width and depth are represented by a single variable, “D” (shown in FIG. 11A), which is the effective diameter of the narrow end of the nanofunnel (equivalent to the nanochannel cross-section dimensions, y is the width or depth of the nanofunnel at position x along the longitudinal (x) axis (also known as the symmetry or longitudinal centerline axis). The variable x₀ indicates the coordinates of the nanofunnel apex, which is also the intersection of the narrow end of the nanofunnel with the nanochannel. Equation 1 therefore reflects that the nanofunnel is seamlessly interfaced with the nanochannel because the nanofunnel critical dimensions are equivalent to those of the nanochannel when x=x₀.

$\begin{matrix} {{\frac{y}{D} = \left( \frac{x}{x_{0}} \right)^{\alpha}},{x > x_{0}}} & {{EQUATION}\mspace{14mu} 1} \end{matrix}$

However, it is noted that Equation 1 is provided for example only as there are other equations of similar form that could be used to stretch or compress the nanofunnel while maintaining the same alpha. Thus, any suitable power law equation can be used to select dimensions for different desired exponents (α) according to what behavior or molecule is targeted for analysis, based on the proportional relationship: y˜x^(α). Here “y” is understood to represent either of the dimensions width or depth. In some embodiments, the width and depth may be defined by the same function of x, yielding a nanofunnel with an aspect ratio (depth:width) of 1 along its entire length. In other embodiments, the width and depth may be defined by different functions of x, yielding a nanofunnel with an aspect ratio other than 1 (e.g., 0.1, 0.2, 0.5, 2, 4) along its entire length or an aspect ratio that varies along the nanofunnel's length.

Again, as shown with FIGS. 11G and 11F, the nanofunnel 20 can have a shape defined by a concatenation of functions (y₁, y₂, y₃, . . . ) where the width and depth of the nanofunnel are defined by y₁ between axial coordinates x₀ and x₁, by y₂ between axial coordinates x₁ and x₂, by y₃ between axial coordinates x₂ and x₃, and so on. Each segment of the nanofunnel can be seamlessly or discontinuously connected to its neighboring segments and the narrow end of the nanofunnel can be seamlessly connected to a corresponding aligned nanochannel or microchannel. The concatenated nanofunnels can consist of 2 to 10 segments in some embodiments or can form long fluidic conduits consisting of up to hundreds or thousands of segments in other embodiments.

As shown in FIG. 11E, the funnel 20 can have a configuration where the exponent α can itself be a function of axial position x. This can create more complicated funnel shapes. FIG. 11E shows a simple example with an exemplary function where the exponent alpha is a function of x. By having the funnel shape defined using a proportionality, y˜x^(α(x)), a variety of scaling factors and constants can be used to adjust the funnel dimensions. In this example, y˜x^((0.015x+1)) (i.e., α(x)=0.015x+1), but other scaling factors and exponent multipliers can be used with y dimension proportional to the x dimension. Furthermore, as shown in FIGS. 11F and 11G, nanofunnels can be configured as a series of segments where the dimensions in each segment are defined by a different geometric relationship and where the segments are connected seamlessly (FIG. 11F) or discontinuously (FIG. 11G). FIG. 11A maps an idealized cylindrical funnel onto a coordinate axis to illustrate the functional form, y˜x^(α). Funnels for which α<1 are convex, while those for which α>1 are concave. FIG. 11B shows a series of funnel shapes having different a exponent values. While the power law function allows investigations over a variety of nanofunnel shapes by varying one parameter, it should not be construed as the exclusive set of funnel geometries that can be fabricated or assessed theoretically. FIGS. 11C, 11D show how the voltage, V, varies along the length of a nanofunnel when α<0.5 (FIG. 11C) and when α>0.5 (FIG. 11D). In these plots, a larger slope in the curve corresponds to a higher electric field at the position, x. When α<0.5 (FIG. 11C), the voltage increases linearly along the entire nanofunnel length and can do so indefinitely. When α>0.5 (FIG. 11D), the voltage can reach a maximum value, v_(∞), within the nanofunnel, above which the voltage will not increase. To be clear, there are changes in nanofunnel behavior that occur when alpha<0.5 and when alpha>0.5, including the voltage profile within the nanofunnel 20 (FIGS. 11C and 11D, bottom plots) and the monomer density profile within the nanofunnel (FIGS. 12A and 12B, bottom plots).

The nanofunnel shown in FIG. 11C has an alpha=0.3 value while that shown in FIG. 11D has an alpha=0.7 to illustrate the noted changes in behavior, not the convex or concave nature of the funnels themselves. In addition to an understanding of shape-controlled force fields, theoretical predictions of DNA behavior can consider the properties of the DNA molecule, specifically its stiffness and length. FIG. 12 shows one important way in which the properties of DNA can affect the operational parameters of trapping and critical transport voltages. Due to the voltage profile in a nanofunnel with α<0.5, the electrostatic force on the trailing end of the DNA molecule acts like a piston, compressing the leading end of the molecule, pushing it towards the nanochannel entrance, and lowering the critical voltage needed to drive transport. This compression results in a plateau region in the plot of monomer concentration, c, as a function of position in the nanofunnel (FIG. 12A). In a nanofunnel with α>0.5, most of the electrostatic force is on the leading end of the molecule and there is no piston effect. In this case, the monomer concentration does not exhibit a compressed plateau region (FIG. 12B).

The theory that was developed to describe DNA molecular behavior in nanofunnels was used to predict trends in a molecule's position, its length, and the critical electric field required to drive transport through the nanochannel. The theoretical predictions are compared to simulation and experiment results. FIG. 13A compares theory (lines) and simulation results (markers) describing the position of a DNA molecule's leading end (x_(i)) as a function of applied voltage (proportional to E₀, the electric field magnitude in the nanochannel). Per standard protocol in theoretical polymer physics, these values are normalized and plotted as dimensionless variables where b is the characteristic DNA Kuhn length, q is the charge on the DNA, D is the geometric average of the nanochannel width and depth, k is Boltzmann's constant, and T is temperature. Results are plotted for DNA molecules that are 200 (diamonds) and 600 (circles) Kuhn lengths long, or approximately 20 and 60 μm, respectively. FIG. 13B shows the position of the DNA molecule's trailing end (x_(f)) as a function of applied voltage. The equilibrium length of the DNA molecule can be determined by the difference, x_(f)−x_(i). FIG. 14 shows a comparison of theory and simulations describing the dependence of the critical electric field required to drive transport through the nanochannel on the power law exponent, α. The dimensionless variable of the plot ordinate is the critical field with the nanofunnel E_(c) ^(f), normalized by the critical field necessary to drive transport through a nanochannel with no funnel, E_(c).

Experimental investigations were conducted to determine the behavior of DNA molecules in a nanofunnel. Similar to the theoretical efforts, the parameters that were measured included the voltage range of stable trapping, the position of a trapped DNA molecule, its equilibrium length, and the critical electric field at which transport through the nanochannel occurs. Fluorescently stained λ-phage and T4-phage DNA molecules were electrokinetically driven into a funnel at field strengths greater than E_(min). The position of the molecule within the nanofunnel was monitored, typically for over 30 min, and plotted as a function of time. This data acquisition protocol was repeated over a range of voltages within the stable trapping regime to determine the dependence of the molecule's position and length on the applied voltage. FIG. 15 are graphs and images from a trapping experiment. DNA molecules were trapped in the nanofunnels shown in FIG. 15A, Fluorescence images were recorded (FIG. 15B) and reduced to an intensity profile (FIG. 15C) characterizing DNA length and position. FIG. 15D shows a time series of these frames highlighting the thermal fluctuations in the molecule's length and position. FIGS. 16 and 17 are graphs of the voltage dependence of trapping position for two DNA molecules having different contour lengths (λ-phage, ˜20 μm long, and T4-phage DNA, ˜70 μm long) in an electrophoresis buffer and in some instances, as indicated, containing 2% by weight of a low molecular weight polymer, polyvinylpyrrolidone (PVP). FIG. 18 is a related graph that illustrates the relationship between the voltage-dependent properties of DNA length and trapping position. These two values are correlated because the greater confinement experienced by the DNA molecule as it is driven deeper into the funnel results in greater extension. The variances in these parameters provide a measure of the trap stability vis-à-vis thermal fluctuations. Each data point in FIGS. 16-18 represents the average of over 20,000 measurements collected over about 30 minutes.

It is contemplated that the use of properly shaped and sized funnels 20 can facilitate macromolecule capture, trapping, and transport through nanochannels 30 having critical dimensions smaller than the radius of gyration of the molecule. By lowering the threshold force needed to drive translocation, greater control over molecular transport dynamics may be achieved. For channels 30 with nanoscale dimensions in width and depth, confinement of the macromolecule in both of these dimensions is disfavored by an entropic energy barrier. Therefore, the optimal funnel geometry can provide a gradual increase in confinement in both dimensions. This can be achieved by patterning funnels using FIB milling in which the lateral dimensions and shape of the funnel are controlled by the pattern over which the beam is rastered. The depth of the funnel is controlled by varying the dwell time of the ion beam, milling deeper features at the funnel mouth and gradually shallower features towards the intersection of the funnel and nanochannel. The introduction of such funnels at the entrance to nanochannels has been predicted theoretically and verified experimentally to reduce the voltage that must be applied to electrokinetically drive double-stranded DNA through long FIB-milled nanochannels. Additionally, given appropriate funnel geometries and capture forces, single molecules can be stably trapped and investigated for a desired length of time.

The devices 10 and/or nanofunnels 20 can be configured to analyze a DNA molecule, a protein, a fluorescently stained molecule, and optionally the analyte molecule can be been modified in any way to provide or enhance analyzing the molecule in a respective nanochannel 20.

The use of FIB milling to fabricate features with control in all three dimensions provides an ultimate degree of flexibility in funnel design. A macromolecule can be gradually driven through an FIB-milled funnel directly into a nanochannel, transitioning from an unconfined to a highly confined state. This gradual transition can result in translocations occurring at low molecular velocities in which the molecule preferentially enters the nanochannel in an unfolded, extended state.

The use of funnels to facilitate the threading of macromolecules into nanochannels lowers the threshold force needed to drive translocation and thus lowers the transport velocity, which is expected to enable more precise optical and electrical measurements on single confined molecules, One example is the sequencing of DNA molecules in a nanochannel interfaced to opposed tunneling probes in which base calling is achieved by measuring the unique tunneling currents through the individual nucleotides. Such a funnel could also be used in isolation (without interfacing it to a long nanochannel) as a conduit between two microchannels and serving as a stochastic sensor. Translocations through the funnel could be monitored optically (e.g. fluorescently stained molecules) and/or electrically (e.g., axial ionic current). A potential advantage to this geometry is the seamless integration of microfluidic and nanofluidic components on a single layer device, in contrast to stacked devices that integrate microfluidic channels and nanoporous membranes. Funnels 20 in which both the width and depth vary gradually are also believed to be suitable, potentially ideal, platforms upon which to study the physical properties of flexible or deformable macromolecules. Because the FIB milled nanochannels and nanofunnels are easily interfaced with other fluidic components on a single chip their use can be integrated with other technologies such as flow injection, separations in microfluidic channels, and single cell lysis.

The described nanofabrication methodology and devices have application to microelectronics and nanofluidics technology. Nanofluidic implementations with nanochannels of these critical dimensions and quality are well suited for a number of applications including single molecule detection and identification, confinement and manipulation of biopolymers, biological assays, restriction mapping of polynucleotides, DNA sizing, physical methods of genomic sequencing, and fundamental studies of the physics of confinement.

FIG. 19 is a schematic illustration showing experimental evaluations of translocation event frequency for DNA molecules electrokinetically driven through the nanochannel from either the funnel side (right to left in FIG. 19) or the channel side (left to right in FIG. 19). FIG. 20 shows the experimental results of the two experiments shown in FIG. 19. The linear increase of translocation event frequency with applied voltage at higher voltages indicates that voltages in this range exceed the entropic barrier value. In the case of translocations originating from the channel side, the exponential region of the data seen at low voltages indicates the presence of an entropic barrier. This barrier is not observed in translocations originating from the funnel side. FIG. 21 is a fluorescence microscopy image that shows further evidence for the existence of an energy barrier to translocation from the channel side. By applying a voltage (0.5 V) below the threshold for an extended period (1.5 hours), DNA molecules were electrophoretically driven to the nanochannel entrance but the force on the molecules was insufficient to drive translocation. This condition results in DNA concentration at the nanochannel side. The critical electric fields, E_(c), to drive DNA transport into and through the nanochannels for different nanofunnel geometries and DNA samples are presented in the table below. All of the nanofunnels have the same length and have a width×depth that increases from about 100 nm×about 100 nm at the nanochannel end (equivalent to the nanochannel width×depth) to about 1.5 μM×about 1.5 μm at the nanofunnel entrance that is interfaced to the microchannel. The nanofunnels differ in the exponent, α, that defines their shape.

TABLE 1 ELECTRIC FIELD REQUIRED TO DRIVE DNA INTO NANOCHANNEL CRITICAL ELECTRIC FIELD FOR EACH DNA SAMPLE (V/cm) λ-PHAGE T4-PHAGE CIRCULAR NANOFUNNEL (~20 μm (~70 μm CHAROMID DNA SHAPE length) length) (~18 μm circumference) α = 0 65 ± 7 65 ± 7 65 ± 7 α = 0.5 16.1 ± 0.7 17.5 ± 0.7 21.7 ± 0.7 α = 1 10.8 ± 0.7 10.8 ± 0.7 12.3 ± 0.7

In order to compare different funnel geometries in these experiments, and to compare experimental results to theoretical predictions, the electric field in the funnels and nanochannels can be compared. To determine these fields, the nanochannel and nanofunnel shape (width and depth) can be precisely determined using atomic force microscopy (FIGS. 22A, 22B), SEM imaging (FIGS. 3B, 3C, 7A, 7B, 7C, 23), and ion beam tomography, for example. The optimal shape(s) may change for macromolecules having different physical properties, systems with different polymer-solvent intermolecular interactions, and driving forces with different flow profiles, all parameters that can be investigated theoretically.

FIG. 23 illustrates a bitmap image 20 bm used to create a corresponding FIB milled funnel 20 and nanochannel 30 (SEM image) with a length of about 22 μm and a graph of an AFM (Atomic Force microscopy) image of width (μm) versus length (μm).

FIG. 24 is a graph showing a parabolic relationship of depth and width over a length of the nanofunnel 20 according to some embodiments of the present invention. That is, the nanofunnel(s) 20 can be configured to have both width and depth dimensions that vary in a parabolic, linear manner over its length according to some embodiments of the present invention.

FIG. 25 shows AFM images of nanofunnels defined by a power law function with a values of 0, 0.5, and 1. Devices incorporating such nanofunnels were used to determine the results represented in the table above. The gray or color scale labeled “Depth (μm)” on the right hand side of the figure shows how the intensities of the nanofunnel profiles on the left hand side of the figure correspond to nanofunnel depth.

Because these characterizations of nanofunnel dimensions provide an accurate determination of electric field strengths through the nanochannel/nanofunnel conduit, direct comparisons between experimental results and theoretical predictions can be made. FIG. 26A illustrates the comparison between the experimentally determined positions of the leading and tailing ends of a trapped λ-phage DNA molecule. FIG. 26B illustrates the comparison between the experimentally determined positions of the leading and tailing ends of a trapped T4-phage DNA molecule. FIG. 27 is a schematic illustration of an analysis system 100 which includes at least one device 10 with at least one nanofunnel 20, electrodes 70 and a control circuit 101 with a funnel applied voltage mode and a channel applied voltage mode, the funnel mode configured to apply a larger voltage than the channel mode.

FIG. 28 is a schematic illustration of a fabrication system 201 with a milling apparatus 200 and a circuit 200 c with a nanofunnel patterning file 200 f which can be totally onboard the apparatus 200, partially onboard the apparatus 200 or remote from the apparatus such as in one or more servers 225.

The foregoing is illustrative of the present invention and is not to be construed as limiting thereof. Although a few exemplary embodiments of this invention have been described, those skilled in the art will readily appreciate that many modifications are possible in the exemplary embodiments without materially departing from the novel teachings and advantages of this invention. Accordingly, all such modifications are intended to be included within the scope of this invention as defined in the claims. The invention is defined by the following claims, with equivalents of the claims to be included therein. 

1. A method of forming a chip with fluidic channels, comprising: forming at least one nanofunnel with a wide end and a narrow end into a planar substrate, the nanofunnel having a length, with width and depth dimensions that both vary over its length; and forming at least one nanochannel or microchannel into the planar substrate at an interface adjacent the narrow end of the nanofunnel.
 2. The method of claim 1, wherein the forming the at least one nanofunnel is carried out using milling directed by an electronic patterning file configured to direct a milling to have a defined dwell time at defined X and Y coordinates to generate the nanofunnel width and depth dimensions over its length.
 3. The method of claim 1, wherein the forming steps are milling steps are carried out using focused ion beam (FIB) milling.
 4. The method of claim 1, wherein the forming the at least one nanofunnel and the forming a corresponding aligned one of the at least one nanochannel or microchannel are both carried out during a single milling operation using a Focused Ion Beam (FIB) milling device that transmits an FIB beam into the substrate and an electronic pattering file that controls a dwell time of the FIB beam at X and Y coordinates to seamlessly connect the nanochannel or microchannel to the narrow end of the nanofunnel.
 5. The method of claim 1, wherein the at least one nanofunnel width and depth dimension vary in a defined geometric relationship over substantially an entire length of the respective nanofunnel to alter a cross-sectional size of the funnel by at least a factor of two from the wide end to the narrow end.
 6. The method of claim 1, wherein the at least one nanofunnel is comprised of a concatenated series of portions in which a respective width and depth dimension vary in a defined geometric relationship over an entire length of each portion, wherein the width and depth of each portion is defined by a different geometric function, and wherein neighboring portions are seamlessly or discontinuously connected.
 7. The method of claim 1, wherein the nanofunnel comprises at least a portion with a substantially parabolic contour.
 8. The method of claim 1, wherein the nanofunnel comprises at least a portion with a substantially convex contour.
 9. The method of claim 1, wherein the nanofunnel comprises at least a portion with a substantially concave contour.
 10. The method of claim 1, wherein the nanofunnel has walls that angle inward at a constant slope.
 11. The method of claim 1, wherein the at least one nanochannel or microchannel has a substantially constant width and depth, and wherein the narrow end of a respective nanofunnel has width and depth dimensions that substantially match a respective width and depth dimension of an aligned corresponding nanochannel or microchannel.
 12. The method of claim 1, wherein the forming the nanofunnel step is carried out by milling, and wherein the method further comprising, before milling the nanofunnel, providing an electronic patterning file that defines dwell times at defined X and Y coordinates to generate the nanofunnel width and depth dimensions over the nanofunnel length, and wherein the providing is carried out to generate a nanofunnel configuration with dimensions with an associated exponent “α” defined by a power law (width, depth ˜x^(α)), where x is an axial coordinate and alpha is a positive number.
 13. The method of claim 1, wherein the nanofunnel has a shape with a power law exponent α configured as a function of axial position x, where y˜x^(α(x)).
 14. The method of claim 1, wherein the at least one nanofunnel is a plurality of nanofunnels and each has a length that is between about 1 μm to about 100 μm.
 15. The method of claim 1, further comprising sealing a flat cover to the substrate to define a nanofluidic chip.
 16. The method of claim 15, wherein the nanofluidic chip is adapted to analyze a molecule of DNA, proteins or other polymeric material.
 17. A device for analyzing molecules such as nucleic acids, comprising: a nanofluidic chip comprising a plurality of nanofunnels, wherein each nanofunnel has a wide end and a narrow end and a length and varies in depth and width along the length. 18-28. (canceled)
 29. A method of analyzing an analyte, comprising: providing a chip with at least one nanofunnel that merges into a corresponding nanochannel; applying a first voltage to cause an analyte to flow into a fluid nanofunnel; then applying a second smaller voltage to cause the analyte to flow into a corresponding nanochannel; and electronically analyzing the molecule in the nanofunnel and/or nanochannel. 30-35. (canceled)
 36. A fluidic analysis system for analyzing molecules, comprising: a fluidic chip comprising a plurality of nanofunnels, each funnel merging into at least one respective nanochannel; and a control circuit in communication with the chip configured to (i) apply a first defined transport voltage to cause a molecule to enter at least one nanofunnel then (ii) apply a defined second transport voltage that is less than the first defined transport voltage to cause the molecule to flow into a corresponding nanochannel. 37-44. (canceled)
 45. A method of analyzing a molecule, comprising: providing a device with at least one nanofunnel; flowably introducing a target molecule into the nanofunnel; trapping the target molecule in the nanofunnel for a time to spatially localize the analyte molecule; and analyzing the analyte molecule in the nanofunnel. 46-49. (canceled)
 50. A Focused Ion Beam (FIB) milling system, comprising: a FIB milling apparatus in communication with or comprising at least one electronic patterning file configured to generate a nanofunnel in a target substrate.
 51. (canceled) 